Chopin Airport is served by two SKM Szybka Kolej Miejska (Fast Urban Railway) lines: S2 and S3. Both of them have a stop in the city center (S2 – Warszawa Śródmieście, S3 – Warszawa Centrum (Central Railway Station)).
More information: here and here

Warsaw Modlin Airport – connection
You can get from the airport to the city center by bus here

Access to University of Warsaw
To University of Warsaw you can get directly from the Warsaw Chopin Airport by bus 175.
To University of Warsaw you can get by metro (M2, station: Nowy Świat – Uniwersytet) or by bus 102, 105, 111, 116, 128, 175, 178, 180, 222, 503, 518, E-2 (bus stop – Uniwersytet).